Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian
Abstract
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second eigenvector of a matrix defined solely in terms of the incidence matrix, called the graph Laplacian. For sparse graphs, the eigenvector can be efficiently computed using the Lanczos algorithm. This graph partitioning algorithm is extended to provide a complete hierarchical subdivision of the graph. The method has been implemented and numerical results obtained both for simple test problems and for several grid graphs.
Cite
@article{arxiv.math/0003036,
title = {Partitioning Sparse Graphs using the Second Eigenvector of their Graph Laplacian},
author = {David De Wit},
journal= {arXiv preprint arXiv:math/0003036},
year = {2025}
}
Comments
Unpublished PGDipSc thesis in the Department of Mathematics at The University of Queensland, Australia. Thesis submitted June 1991. Minor textual modifications to original version. 56 pages, 2 tables, 21 figures. <http://www.kurims.kyoto-u.ac.jp/~ddw/>